Causally inconsistent biological networks, spanning trees, and results of the SST algorithm. (A) The incoherent feed-forward loop (IFFL) as an example of a causally inconsistent network, termed an "unbalanced graph" in graph theory. (B) The three spanning trees corresponding to the IFFL shown in (A). (C) Magnification of neighborhood of the TXNIP feedback loop from the "Hypoxic Stress" network. The effective node weights Sn → REF from SST are indicated in the boxes, and the red X indicates the edge that is absent in the pruned causally consistent version of the network. (D) Receiver operating characteristic (ROC) curve (true positive rate vs. false positive rate) for the comparisons between the effective node weights Sn → REF from SST and the corresponding nodal signs sn → REF for the 19 networks given in Additional file1: Table S1. The color of the curve follows the prediction threshold applied on Sn → REF and shows that mislabeling occurs mainly for small values around zero (i.e. the green part of the curve). The area under the ROC curve (AUROC) is 0.992.